What is the significance of this Stanford University "Financial Market Time Series Prediction with RNN's" paper?
After a very brief look at the paper, I think that they are predicting the stock price for the next day, and not for the current day, which is quite common and reasonable: see equation (1), where they predict $x(t+1)$.
So I don't see any issue with this paper.

But I've only quickly looked at it, so I may have missed something, of course.